Data-Driven Analysis and Predictive Control of Descriptor Systems With Applications

Despite growing interest in data-driven analysis and control of linear systems, descriptor systems (or singular systems) - which are essential for modeling complex engineered systems with algebraic constraints like power and water networks - have received comparatively little attention. This paper develops a comprehensive data-driven framework for analyzing and controlling discrete-time descriptor systems without relying on explicit state-space models. We address fundamental challenges posed by non-causality through the construction of forward and backward data matrices, establishing data-based sufficient conditions for controllability and observability in terms of input-output data, where both R-controllability and C-controllability (R-observability and C-observability) have been considered. Building on them, we then extend Willems' fundamental lemma to incompletely controllable descriptor systems. These methodological advances Data-Enabled Predictive Control (DeePC) for descriptor systems to achieve output tracking and to maintain performance under incomplete controllability conditions, as demonstrated in two case studies: i) Frequency regulation in an IEEE 9-bus power system with 3 generators, where DeePC maintained the frequency stability of the power system despite deliberate violations of R-controllability, and ii) Pressure head control in an EPANET water network with 3 tanks, 2 reservoirs, and 117 pipes, where output tracking was successfully enforced under algebraic constraints. Note to Practitioners - Algebraic constraint problems are common in practical engineering systems, such as power balance constraints in electrical networks and flow-pressure coupling relationships in water distribution networks. Such systems are typically modeled using descriptor systems (also known as singular systems). However, traditional analysis and control for these systems have relied on explicit mathematical models, making rapid deployment challenging in scenarios with complex structures or unknown dynamics. This paper proposes a purely data-driven framework that enables performance analysis (including controllability and observability) and tracking control for descriptor systems without requiring explicit mathematical models. The aim is to facilitate the design of reliable controllers even when accurate system models are incomplete or unavailable.